A simple model of the hurricane boundary layer revisited

A simple slab model for the boundary layer of a hurricane is re-examined and a small error in the original calculation is corrected. With this correction, the development of supergradient winds is a ubiquitous feature of the solutions. The boundary layer shows two types of behaviour in the inner core of the vortex depending on the depth of the layer and the maximum tangential wind speed above the layer. For small depths and/or large tangential wind speeds, large supergradient winds develop and lead to a rapid deceleration of the inflow such that the inflow becomes zero at some radius inside the radius of maximum tangential wind speed above the boundary layer. For large depths and/or small tangential wind speeds, the solutions do not become singular until within a few kilometres of the rotation axis. The transition between the two regimes is very abrupt. Interpretations are given for the foregoing behaviour. Other aspects of the boundary-layer dynamics and thermodynamics are investigated including: the dependence on mixing by shallow convection; the effects of a radially varying boundary-layer depth; the effects of downward momentum transport; the dependence of thermodynamical quantities on the boundary-layer depth; and the radial variation of equivalent potential temperature. Predicted values of the last quantity are in acceptable agreement with observations made in category-five hurricane Isabel (2003). The version with radially varying depth gives more realistic vertical velocities in the inner-core region of the vortex. The limitations and strengths of the slab model are discussed. Copyright (c) 2008 Royal Meteorological Society.